Matrices and Determinants
Inverse of a Matrix
Premium Question
Grade 12
Question:
If $A$ is an invertible square matrix, then $(A^{-1})^{-1}$ equals:
(1) $A$
(2) $A^{-1}$
(3) $I$
(4) $A^T$
Step-by-Step Solution
Key Concept: The inverse of a matrix is defined so that $A \cdot A^{-1} = A^{-1} \cdot A = I$ — apply this same defining relation to the matrix $A^{-1}$ itself and identify which matrix plays the role of "the inverse of $A^{-1}$".
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)